abbot: solar constant of radiation 91 



If ^0 be the intensity of the original beam before entering the 

 transparent medium whose transmission is to be investigated, 

 then after the passage through the first stratum of unit thickness 

 let us suppose a fraction of the original, represented by p, has 

 passed through, so that what was A o becomes A op. Then since 

 a second stratum identical with the first in constitution and 

 thickness must, according to Bouguer's assumption, have an 

 identical effect, the ray which was Ao will emerge from the sec- 

 ond stratum Aop~, and so on. The fraction p transmitted by 

 the unit of thickness is the common ratio of a geometric progres- 

 sion, so that after passing through a thickness m of the medium, 

 the intensity of the light which was formerly Ao will become 

 AoP". 



As the height to which the atmosphere extends in appreciable 

 density is very small compared with the radius of the earth, 

 the thickness of the layer traversed by a solar beam of a zenith 

 distance not exceeding 70° is approximately proportional to the 

 secant of the zenith distance of the sun at the time of observa- 

 tion. If we regard unit thickness as that corresponding to a 

 barometric pressure of 760 mm. of mercury, then p in our for- 

 mula corresponds to the vertical transmission coefficient of the 

 atmosphere above sea-level, and for any station where the baro- 

 metric pressure is B the intensity of the ray from the sun as it 

 reaches the earth's surface, which we call A, may be expressed 

 by the formula. 



A = Aop ^ 



760 ^®°^' 



Some writers have preferred to use the formula as a formula 

 of "absorption" rather than of transmission. In that way the 

 expression reduces to a somewhat different form, but its funda- 

 mental principles are the same. The investigations of Herschel, 

 Forbes, Pouillet and others up to the time of Langley had refer- 

 ence to this exponential formula, based upon the hypothesis of 

 Bouguer, which was to the effect that successive equal layers of 

 transparent material transmit equal fractions of the incident ray. 



A convenient method of applying the atmospheric transmis- 

 sion formula is to take logarithms of both members of the equa- 



